Time-frequency feature extraction and separation method of frequency hopping signal under multi-feature constraint

Abstract

The application discloses a time-frequency feature extraction and separation method of frequency hopping signals under multi-feature constraints, which carries out pretreatment on a wideband mixed signal through a Chebyshev I type band-pass filter, filters out out-of-band interference and improves a signal-to-noise ratio; designs an optimal window length based on the double constraints of a fixed pulse width and a bandwidth of a target signal, generates a gray time-frequency spectrum with balanced time-frequency resolution through STFT; constructs a dynamic double threshold value through global and local gray feature modeling, realizes accurate segmentation and edge repair of signals and noises in combination with 8-neighborhood correlation discrimination; designs a customized rectangular structure element based on target signal parameters, eliminates noise and fills up signal defects through morphological opening and closing operation; constructs a multi-feature constraint system and a progressive strategy of 'primary screening-secondary screening-tertiary screening', screens target connected components and reconstructs complete target frequency hopping signals through inverse STFT. Through multi-feature collaborative constraints in the whole process, the application improves the signal detection rate and separation precision in the low signal-to-noise ratio and multi-interference scene.

Description

Technical Field

[0001] This invention belongs to the field of frequency hopping signal processing technology, specifically relating to a method for time-frequency feature extraction and separation of frequency hopping signals under multiple feature constraints. Background Technology

[0002] In existing technologies, the detection and separation of frequency-hopping signals typically rely on time-frequency analysis techniques. These techniques involve time-frequency transformation, denoising and segmentation, feature selection, and signal extraction to extract the time-frequency features of the target signal from a complex electromagnetic environment, thus meeting the needs of subsequent parameter estimation, signal identification, and location tracking. However, existing processing methods have some significant shortcomings in terms of time-frequency matching accuracy, adaptability to low signal-to-noise ratios, feature protection effectiveness, and anti-interference capabilities.

[0003] In practical applications, frequency-hopping signals often have fixed bandwidth and fixed pulse width characteristics, and are susceptible to multipath effects, channel attenuation, environmental noise, and various types of interference such as fixed-frequency, frequency-sweeping, and burst interference. This leads to uneven grayscale distribution in the time-frequency spectrum, local energy loss in the signal, and overlap between interference and target signal features. Existing processing methods often use general window functions for time-frequency transformation, fixed thresholds for binarization segmentation, and general structuring elements for morphological denoising. They also rely on single or limited-dimensional features for screening. Due to these factors, phenomena such as time-frequency resolution imbalance, signal edge breaks, distortion of key features, and misjudgment of interference signals can easily occur, ultimately resulting in low target signal detection rate and insufficient separation accuracy.

[0004] Therefore, it is evident that existing technologies still suffer from problems such as mismatch between time-frequency resolution and signal parameters, poor threshold adaptability under low signal-to-noise ratio, insufficient protection of signal morphological features, and low screening accuracy in multi-interference scenarios. These are the shortcomings of existing technologies.

[0005] In view of this, it is very necessary to provide a method for time-frequency feature extraction and separation of frequency hopping signals under multiple feature constraints to solve the above-mentioned defects in the prior art. Summary of the Invention

[0006] The purpose of this invention is to address the shortcomings of existing technologies, such as mismatch between time-frequency resolution and signal parameters, poor threshold adaptability under low signal-to-noise ratio, insufficient protection of signal morphological features, and low screening accuracy in multi-interference scenarios. This invention provides a method for time-frequency feature extraction and separation of frequency-hopping signals under multi-feature constraints to solve the aforementioned technical problems.

[0007] To achieve the above objectives, the present invention provides the following technical solution: This invention provides a method for time-frequency feature extraction and separation of frequency-hopping signals under multiple feature constraints, specifically including the following steps: Step S1: Receive the external broadband mixed signal through the radio frequency receiving module, record the original parameters of the received signal, synchronously obtain the prior parameters of the target frequency hopping signal, select Chebyshev Type I bandpass filter as the core filter device, perform pre-filtering processing on the received broadband mixed signal, and output the filtered time domain signal. Step S2: Select STFT as the time-frequency image generation tool, calculate the optimal window length based on the prior parameters of the target frequency hopping signal with dual constraints, and output the time-frequency optimized grayscale time-frequency image; Step S3: Model the global and local grayscale features of the grayscale time-frequency image output in step S2. Based on the global and local grayscale features, design two dynamic thresholds, a high threshold and a low threshold, to construct a dual screening mechanism. Based on the binarization decision rule, repair the signal edge by judging the neighborhood correlation and output the binarized image. Step S4: Input the binarized image output in step S3, design the structural elements; after processing by opening and closing operations, introduce a morphological fault tolerance mechanism, quantify and verify the processing effect, and output a morphologically optimized binary image. Step S5: Detect the connected components in the morphologically optimized binary image output in step S4, construct a multi-feature constraint system, and use a progressive strategy to filter the target connected components; based on the time-frequency position of the target connected components, extract the original STFT time-frequency sub-matrix, restore it to the time domain signal segment through inverse STFT transformation, and splice it in time order to form a complete target frequency hopping signal.

[0008] Furthermore, in step S1, based on the fixed parameter characteristics of the target frequency-hopping signal, the frequency components corresponding to the target frequency-hopping signal are selectively retained, out-of-band noise and narrowband interference are filtered out, and the signal purity and signal-to-noise ratio in the subsequent time-frequency image generation stage are improved. This provides high-quality preprocessing input for the entire process of time-frequency feature extraction and separation of the frequency-hopping signal. Specifically, this is implemented as follows: Step S11: Receive external broadband mixed signals through the radio frequency receiving module. The broadband mixed signals include at least target frequency hopping signals, environmental thermal noise, fixed frequency interference, frequency sweeping interference, and burst pulse interference, covering typical interference types in complex electromagnetic environments. Record the raw parameters of the received signal, including the signal sampling frequency. and quantization bits, where the sampling frequency Strictly satisfying the Nyquist criterion, i.e. This ensures that the target signal is sampled without aliasing. The number of quantization bits is used to ensure the quantization accuracy of the signal and avoid signal feature distortion caused by quantization distortion.

[0009] The prior parameters of the target frequency-hopping signal are acquired synchronously. These prior parameters are inherent characteristic parameters of the target frequency-hopping signal and can be obtained through system presets or prior signal analysis and measurement. They include at least a fixed bandwidth B, a fixed pulse width T, and a preset center frequency. and frequency hopping interval This provides a parameter benchmark for subsequent signal processing; Based on the fixed bandwidth B of the target frequency-hopping signal, the passband range of the bandpass filter is determined, denoted as:

[0010] in, It is the fixed bandwidth of the target frequency hopping signal. The center frequency of the target frequency hopping signal.

[0011] The passband range only allows the target frequency-hopping signal to pass through, suppressing interference signals and environmental noise outside the passband.

[0012] Step S12: Select a Chebyshev Type I bandpass filter as the core filter component to perform pre-filtering processing on the received broadband mixed signal; the Chebyshev Type I bandpass filter has the technical advantages of low passband ripple, fast stopband attenuation, and convenient engineering implementation, and can efficiently suppress out-of-band interference while ensuring that the amplitude and phase characteristics of the target signal are not distorted. The transfer function of the Chebyshev Type I bandpass filter is defined as:

[0013] in, The value of the passband ripple factor is ≤1dB. The filter order is determined by the stopband attenuation requirement and the stopband cutoff frequency. It is an Nth-order Chebyshev polynomial; The center frequency of the target frequency hopping signal. The frequency value is the frequency component of the broadband mixed signal to be filtered.

[0014] Step S13: Configure the key parameters of the filter. The specific steps are as follows: The passband ripple coefficient ε is set to 0.1 to keep the amplitude fluctuation of the target signal within the passband within 1dB, ensuring that the amplitude characteristics of the target signal are not affected by the filtering process. According to the preset stopband attenuation requirements With stopband cutoff frequency Calculate the filter order using the formula The specific formula is as follows:

[0015] in, For stopband attenuation; B is the stopband cutoff frequency, and B is the fixed bandwidth. This represents the passband ripple factor. Define an Nth-order Chebyshev polynomial This provides mathematical support for the frequency response characteristics of the filter, ensuring stable and controllable filtering performance. The specific expression is:

[0016] Step S14: Based on the transfer function configured with the above parameters, two engineering-equivalent filtering implementation methods are provided to adapt to different application scenarios, and finally output a high signal-to-noise ratio time-domain filtered signal, including frequency domain implementation and time domain implementation. The frequency domain implementation method is used for the received broadband mixed signal. Perform a Fourier transform to obtain the frequency domain signal:

[0017] Where FT stands for Fourier transform; The frequency domain signal X( ) and the transfer function H( Perform a multiplication operation to obtain the filtered frequency domain signal:

[0018] To achieve signal retention within the passband and signal attenuation outside the passband; For the filtered frequency domain signal Performing the inverse Fourier transform yields the time-domain filtered signal:

[0019] Wherein, IFT stands for Inverse Fourier Transform; The time-domain implementation method, for the transfer function Perform an inverse Fourier transform to obtain the impulse response of the filter;

[0020] Where IFT stands for Inverse Fourier Transform; Received broadband mixed signal With impulse response Performing convolution operations directly yields the time-domain filtered signal:

[0021] Where * represents convolution operation.

[0022] Save the filtered time-domain signal , as input signals for subsequent steps; The filtered time-domain signal The signal is stored as input for subsequent steps; the filtering effect is quantized and verified to ensure that the preprocessing step can improve the signal-to-noise ratio to a certain level. Horizontal; among which The total bandwidth of the received signal. The target signal bandwidth is defined; and the out-of-band redundant energy in the time-frequency image is effectively eliminated, meeting the signal quality requirements of subsequent time-frequency image processing.

[0023] Furthermore, step S2, through precise matching design of window length and fixed pulse width and fixed bandwidth of the target frequency hopping signal, generates a high-quality grayscale time-frequency spectrum image with balanced time-frequency resolution and complete target signal features, providing clear and distortion-free time-frequency image input for subsequent binarization, morphological processing, and feature selection; specifically including the following steps: Step S21: Select Short-Time Fourier Transform (STFT) as the time-frequency map generation tool. The STFT is used to represent the joint time-frequency distribution of the target signal. This transform has a simple principle, high computational efficiency, and is convenient for engineering implementation, making it suitable for real-time signal processing scenarios. The mathematical expression of STFT is defined as follows:

[0024] in, This is the filtered time-domain signal; Using the time window center as the sliding variable, the window function moves along the time axis to cover the entire signal duration; For window functions; This is a complex-valued time-frequency matrix, where each row corresponds to a time interval. Column corresponding to frequency , It is a complex exponential factor; Furthermore, a Hamming window is selected as the window function in this invention. The Hamming window has the characteristics of low spectral leakage and narrow main lobe, which can effectively preserve the time-frequency characteristics of the signal; its mathematical definition is:

[0025] in, The window length is the number of sampling points included in the window function. Taking the modulus of the complex-valued time-frequency matrix output by the STFT, we obtain | |, whose value corresponds to the time-frequency point The signal energy intensity at a given location is used to construct the grayscale time-frequency image required for subsequent processing.

[0026] Based on | | The grayscale time-frequency image after time-frequency optimization is constructed as follows:

[0027] in, For the number of pixels on the timeline, Number of pixels on the frequency axis; Step S22: Clarify the quantization requirements for time resolution and frequency resolution, ensuring that they match the fixed pulse width and fixed bandwidth of the target signal, respectively; specifically including: Based on window length and sampling frequency The time-frequency resolution of the STFT is defined to characterize the ability of the STFT to distinguish signals at different times, and directly determines the accuracy of capturing the pulse width of the target signal. Its mathematical expression is:

[0028] Based on window length and sampling frequency Frequency resolution is defined to characterize the ability of an STFT to distinguish signals of different frequencies, and directly determines the completeness of coverage of the target signal bandwidth. Its mathematical expression is:

[0029] Input the prior parameters of the target frequency-hopping signal, including a fixed pulse width T and a fixed bandwidth B; set the frequency axis oversampling coefficient k. 2. Ensure that the target signal bandwidth corresponds to at least two frequency pixels in the time-frequency graph to enhance feature distinguishability; fix the pulse width to match the target signal. With fixed bandwidth Window length It must meet two constraints, including frequency resolution constraint and pulse width matching constraint; The frequency resolution constraint is expressed as follows:

[0030] The pulse width matching constraint is expressed as follows:

[0031] in, Sampling frequency, Here, B is the frequency axis oversampling coefficient, B is the fixed bandwidth, and T is the fixed pulse width. For the length of the window, Frequency resolution; Will Substituting the rate of change and resolution constraints yields:

[0032] Combining pulse width matching constraints, the final window length is designed as follows:

[0033] in, This represents the floor function operator; This window length satisfies the balance requirements of time resolution and frequency resolution, ensuring both the integrity of pulse width capture and sufficient bandwidth coverage, while avoiding distortion of time and frequency characteristics.

[0034] Furthermore, the connected components of the target signal in the time-frequency diagram satisfy the following conditions: when At that time, the number of pixels on the time axis Precisely match pulse width; number of pixels on the frequency axis. , fully covering bandwidth B.

[0035] Furthermore, step S3 achieves dynamic threshold adjustment through joint modeling of global and local grayscale features. Combined with an 8-neighborhood correlation discrimination strategy, it accurately segments the signal and noise in the time-frequency image, repairs the signal edge breakage problem in low signal-to-noise ratio scenes, and provides a complete and clean binary image input for subsequent morphological processing. Specifically, it includes the following steps: Step S31: Perform time-frequency image grayscale feature modeling to provide quantization data support for dynamic threshold calculation. Specifically, this is implemented as follows: Define the grayscale time-frequency image Global grayscale mean μ and global variance The mathematical expressions are as follows:

[0036]

[0037] in, This represents the grayscale value of the pixel in the i-th row and j-th column, corresponding to the signal energy intensity at the time-frequency point (i,j). The larger the value, the more concentrated the signal energy at that time-frequency point. The global grayscale mean μ is used to quantify the average energy level of the entire time-frequency map, providing a basic reference benchmark for dual threshold calculation and preventing the threshold from deviating from the overall energy background. The global variance σ² is used to characterize the dispersion of all pixel grayscale values ​​relative to μ. The larger σ² is, the more significant the energy difference between signal and noise in the time-frequency map and the more uneven the grayscale distribution. Conversely, the smaller the σ² is, the smoother the grayscale distribution. This parameter provides a global basis for subsequent adjustment of the width of the threshold interval. The grayscale time-frequency image Divided into Non-overlapping local blocks ,satisfy:

[0038] Where P is the number of local blocks in the time axis direction and Q is the number of local blocks in the frequency axis direction. The values ​​of P and Q are determined through engineering experiments. The core principle is to ensure that the local blocks can capture local gray-scale differences without disrupting the connectivity of the target signal. The number of pixels on the time axis for a single local block. The frequency axis pixel count of a single local block is used to achieve non-overlapping division of the global image using the above equal division formula; The number of pixels on the time axis of the connected components of the target frequency hopping signal is determined by the fixed pulse width of the target signal and the STFT time resolution. The number of pixels on the frequency axis of the connected components of the target frequency-hopping signal is determined by the fixed bandwidth of the target signal and the frequency resolution of the STFT. The constraint condition is essentially to ensure that each local block can fully accommodate the local region of the connected components of the target signal in both time and frequency dimensions, so as to avoid the target signal features being fragmented due to the small size of the local block, and to ensure that the local feature calculation can truly reflect the local grayscale characteristics of the target signal.

[0039] The local variance of the p-th and q-th local blocks is defined as:

[0040] in, For the p-th, q-th local block The local mean is used to quantify the average energy level of the local block, and complements the global mean μ. Let represent the set of pixel indices belonging to the p-th, q-th local block. This explicitly limits the calculation of the local variance to pixels within the current local block, avoiding interference from pixels across different regions. (Local variance) Used to characterize the dispersion of grayscale values ​​within a single local block, accurately capturing the differences in local energy distribution in different regions of the time-frequency map, for local blocks with concentrated signals. Larger; for noise-dominated local blocks, The parameter is relatively small, which provides key quantitative support for the local adaptive adjustment of the dual thresholds, enabling the thresholds to dynamically adapt to the grayscale distribution characteristics of different regions of the time-frequency map.

[0041] Step S32: Perform an adaptive dual threshold calculation operation based on local variance. Dynamic threshold adaptation is achieved through the fusion of global and local features. Specifically: Design a high threshold based on global and local grayscale features. With low threshold Two dynamic thresholds are used to construct a dual screening mechanism; The high threshold The mathematical expression is:

[0042] The low threshold The mathematical expression is:

[0043] in, , The coefficients were determined through grid search optimization. , This article adopts =2.0、 =0.8; , These are the maximum and minimum values ​​of the variance of all local blocks, respectively, used to reflect the non-uniformity of energy distribution in the time-frequency plot; The dynamism of the dual screening mechanism is reflected in the following: when the variance difference of local blocks is large, that is, when the energy distribution is uneven, the threshold interval is adaptively widened; when the variance difference of local blocks is small, the threshold interval is adaptively narrowed, so as to ensure the threshold adaptability under different signal-to-noise ratio scenarios.

[0044] Step S33: Perform binarization decision rule operation, and repair signal edges through neighborhood correlation to ensure signal feature integrity. Specifically: Define a binarized image as:

[0045] in, =1 indicates a foreground signal pixel. =0 indicates background noise pixels.

[0046] The binary decision rule is:

[0047] in, express The 8-neighbor set of pixels contains the 8 adjacent pixels around the given point. If there are at least N pixels in the neighborhood that satisfy... Then the current pixel is determined to be a signal pixel. Otherwise, it is judged as a noise pixel. This rule addresses the issue of disconnected connected components under low signal-to-noise ratio conditions by utilizing neighborhood correlation, thus ensuring the integrity of signal characteristics.

[0048] Furthermore, in step S4, a rectangular structural element is designed using prior information about the fixed bandwidth and pulse width of the target signal. A morphological fault-tolerant mechanism is introduced, and through the collaborative processing of fault-tolerant opening operations and traditional closing operations, noise and bright spots are efficiently eliminated while ensuring the fidelity of signal edges and the integrity of key features, providing a clean and distortion-free binarized image input for subsequent connected component screening. Specifically, this includes the following steps: Step S41: Define and define the functions of basic morphological operations to provide a theoretical basis for processing. The specific implementation is as follows: Suppose the binarized image after step S3 The structural element is S, and the morphological corrosion is ( ) and expansion ( The operation is defined as follows:

[0049]

[0050] in, Image pixel coordinates, These are the coordinates of the structuring element.

[0051] Opening operation ( ) is defined as "corrosion followed by expansion", and the closing operation ( It is defined as "expansion followed by corrosion"; Step S42: Perform the design operation of the rectangular structural element, and achieve accurate matching between the structural element and the signal features based on the prior parameters of the target signal. Specifically: Based on the fixed bandwidth B and fixed pulse width T of the target frequency hopping signal, and the frequency axis resolution of the time-frequency image. Time axis resolution t; where the frequency axis resolution Defined as the frequency range corresponding to a unit pixel, time axis resolution t is defined as the time length corresponding to a unit pixel; set the rectangular structure element. ; Furthermore, set the width of the structural element. Corresponding to the frequency axis, ensure that the width of the structural element is exactly the same as the number of pixels in the time-frequency image corresponding to the bandwidth of the target signal; the expression is:

[0052] Where B is the target signal bandwidth. Time-frequency image frequency axis resolution; Furthermore, set the height of the structural element. Corresponding to the time axis, ensure that the height of the structuring element perfectly matches the number of pixels in the time-frequency image corresponding to the pulse width of the target signal. The expression is:

[0053] in, To fix the pulse width, t is the time axis resolution of the time-frequency image; The structuring element S adopts a solid rectangle design, meaning that all pixel values ​​within the structuring element are 1, and the coordinates of all pixels within the structuring element satisfy:

[0054] The core logic of this design lies in achieving the specificity of morphological operations through size matching: the erosion operation only eliminates elements smaller than a certain size. × The dilation operation only repairs edge defects in the connected domains of the target signal without damaging the target signal boundary; it does not cause fusion of connected domains of adjacent interfering signals. Furthermore, by adapting the size of the structuring element to the target signal, a morphological fault-tolerant mechanism is constructed, which can adapt to the localized small energy loss caused by channel attenuation in the measured signal, avoiding the problem of traditional general-purpose structuring elements misjudging the missing effective signal portion as noise.

[0055] Step S43: Perform collaborative optimization processing of fault-tolerant opening operation and traditional closing operation to achieve a balance between noise cancellation and signal fidelity. Specifically, this is implemented as follows: Define the binarized image after co-processing as , This method represents a morphologically optimized binary image; it removes noise and bright spots through tolerance-tolerant opening operations, while preserving the connectivity of local energy-deficient regions of the signal using tolerance-tolerant offset; then, it fills in internal holes and edge defects in the signal connected domains using traditional closing operations, thus repairing signal breakage problems in low signal-to-noise ratio scenarios; its transformation expression is:

[0056] Where S is the structural element; To quantify the processing effect, the signal edge fidelity F is defined as the degree of edge overlap between the processed image and the ideal binarized image, expressed as:

[0057] in, For an ideal binarized image, The number of pixels on the time axis of the connected components of the target frequency hopping signal. The number of pixels on the frequency axis of the connected components of the target frequency hopping signal; When F ≥ 0.95, the signal edge distortion is determined to be less than 5%, which meets the signal morphology accuracy requirements for subsequent multi-feature joint screening; if F < 0.95, the structuring element size is fine-tuned. , (Adjustments not exceeding 1 pixel) Re-execute the collaborative operation until the fidelity requirement is met.

[0058] Furthermore, step S5, based on the prior information of the fixed parameters of the target frequency hopping signal, constructs a multi-feature constraint system, accurately identifies the target connected components through a progressive screening strategy, significantly reduces the false detection rate, and provides a clean and effective target region input for subsequent signal reconstruction. Specifically, it includes the following steps: Step S51: Perform connected component detection and core feature quantification definition operations to construct a multi-feature constraint system of "area + aspect ratio + average energy" to provide accurate quantitative basis for screening. Specifically, this is implemented as follows: exist The set of connected components detected in the middle is represented as Where K is the total number of connected components; for each connected component Define a multi-feature constraint system, including the area of ​​connected components, the aspect ratio of connected components, and the average energy of connected components; The area of ​​the connected component is defined as follows: The theoretical value for the total number of pixels contained is:

[0059] in, The number of pixels on the time axis of the connected components of the target frequency hopping signal. B is the number of pixels on the frequency axis of the connected components of the target frequency-hopping signal; B is the bandwidth of the target signal. Time-frequency image frequency axis resolution; To fix the pulse width, t is the time axis resolution of the time-frequency image; The tolerance range for the area of ​​connected components is set as follows in actual screening:

[0060] in, (Lower tolerance limit) (Upper tolerance limit); This article adopts and .

[0061] The aspect ratio of the connected components is defined as follows: Frequency axis pixel count With time axis pixel count The ratio, its theoretical value is expressed as:

[0062] in, The number of pixels on the time axis of the connected components of the target frequency hopping signal. B is the number of pixels on the frequency axis of the connected components of the target frequency-hopping signal; B is the bandwidth of the target signal. Time-frequency image frequency axis resolution; To fix the pulse width, t is the time axis resolution of the time-frequency image; The tolerance range for the aspect ratio of connected components in actual filtering is set as follows:

[0063] in, ; This article adopts and .

[0064] The definition of the average energy of the connected components is as follows: The mean gray level of the corresponding region in the original time-frequency image is defined as:

[0065] in, Area of ​​the connected components; Set energy threshold ,in and These are the global mean and standard deviation of the time-frequency image, respectively, and the selection criteria are: .

[0066] Step S52: Execute a multi-feature progressive filtering strategy design to achieve accurate filtering of target connected components through hierarchical constraints, specifically as follows: A three-level screening logic of "initial screening - secondary screening - final screening" is constructed. Each level of screening is based on specific features to form constraints, gradually eliminating interfering connected components and retaining the target connected components. Initial screening based on the area of ​​connected components To serve as the screening criterion, interfering connected components whose size differs significantly from the target signal (such as extremely small noise bright spots and extremely large interference regions) are quickly eliminated, reducing the computational complexity of subsequent screening; the second screening is based on the aspect ratio of the connected components. As a screening criterion, interfering connected components that "match area but mismatch shape" (such as narrowband long pulse width interference and wideband short pulse width interference) are eliminated to strengthen the constraint on the rectangular shape of the target signal; the final screening is based on the average energy of the connected components. As the selection criterion, low-energy noise residue and weakly interfering connected components are filtered out to ensure that the retained connected components possess the high-energy concentration characteristics of the target signal; its mathematical expression is:

[0067] in, To set a tolerance range for the area of ​​connected components in actual screening. To set a tolerance range for the aspect ratio of connected components in actual screening. The average energy of the connected components. To set an energy threshold; Step S53: Based on the target connected component The time-frequency position is determined, and signal reconstruction is achieved through inverse time-frequency transformation. Let... The time interval corresponding to each connected component is (satisfy ), frequency range is (satisfy The refactoring process includes: From the original time-frequency matrix Extract the corresponding region submatrix ; Perform inverse STFT transformation:

[0068] in, For the time-domain reconstructed signal segment corresponding to the k-th target connected component, For window functions, This is a complex-valued time-frequency matrix, where each row corresponds to a time interval. Column corresponding to frequency t represents the reconstructed time point in the time domain.

[0069] The reconstructed signal segments corresponding to all connected components are spliced ​​together in time sequence to form a complete frequency hopping signal. .

[0070] The beneficial effects of this invention are as follows: By designing the optimal window length through dual constraints, the STFT time-frequency resolution is adapted to the target signal parameters, avoiding truncation or distortion of time-frequency features, and the generated grayscale time-frequency image can completely retain the target signal features; a dynamic dual-threshold mechanism is adopted for joint modeling of global and local grayscale features, and the threshold interval can be adaptively widened or narrowed according to the uneven energy distribution of the time-frequency image, repairing the signal edge breakage problem under low signal-to-noise ratio and improving the signal and noise segmentation accuracy; a customized solid rectangular structural element is designed based on the target signal parameters, and through the collaborative processing of opening operation followed by closing operation, only noise bright spots smaller than the structural element are eliminated, while filling the internal holes and edge defects of the signal connected domain. The constructed morphological fault-tolerant mechanism can adapt to the local small energy loss caused by channel attenuation; a multi-feature constraint system and progressive strategy are constructed to eliminate interference connected components with size mismatch, morphological mismatch, and low energy layer by layer, reducing the false detection rate; a Chebyshev type I bandpass filter is selected, and different application scenarios are adapted through frequency domain or time domain implementation methods to suppress out-of-band noise and various interferences.

[0071] Furthermore, the design principle of this invention is reliable, the structure is simple, and it has a very wide range of application prospects.

[0072] Therefore, it is evident that the present invention has substantial features and progress compared with the prior art, and the beneficial effects of its implementation are also obvious. Attached Figure Description

[0073] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on the provided drawings without creative effort.

[0074] Figure 1 This is a flowchart illustrating a method for extracting and separating time-frequency features of frequency-hopping signals under multiple feature constraints, as provided in this embodiment. Detailed Implementation

[0075] The present invention will now be described in detail with reference to the accompanying drawings and specific embodiments. The following embodiments are explanations of the present invention, but the present invention is not limited to the following implementation methods.

[0076] Example 1: This embodiment uses the publicly available dataset DroneRFb-DIR: A Radio Frequency Signal Dataset for Non-cooperative UAV Individual Identification. A Universal Software Radio Peripheral (USRP) model USRP-2955 is used as the RF receiver, with key parameters configured as follows: sampling rate 80MHz, center frequency 2.44 GHz, and sampling duration of 50ms per signal segment. Before each data acquisition, the UAV is started and paired with the remote controller, setting the UAV's communication frequency band to 2.4GHz.

[0077] Twelve groups of UAV remote control frequency hopping signals encoded as A1, A2, C1, C2, D1, D2, E1, E2, F1, F2, G1, and G2 from the DroneRFb-DIR dataset were selected as target signals. The broadband mixed signals in the dataset contain four typical components: UAV remote control signals (target signals), UAV image transmission signals, Bluetooth signals, and Wi-Fi signals, forming a complex electromagnetic interference environment.

[0078] The signal samples in question are flight control signals from DJI drones. Typical characteristics include a fixed pulse width of 500μs, a fixed bandwidth of 2.34MHz, and the same sweep head and tail structure at the start and end of the signal; a frequency hopping interval of 5MHz; a preset stopband attenuation of 40dB, and a stopband cutoff frequency of 2.44GHz±3MHz.

[0079] After processing by the method in this embodiment, most target frequency hopping remote control signals can accurately form independent connected regions. Only when two or more signals are too close in the time and frequency domain will they merge into a single connected region (which is an inherent limitation of image processing signal extraction methods), but this does not affect the overall separation effect.

[0080] The performance of this embodiment was compared with that of the classic method. The results showed that the detection probability of the algorithm of this invention for 12 sets of UAV remote control signals remained above 0.43, with an average detection probability of 0.638. In contrast, the detection probability of the classic method fluctuated greatly (0.26~0.73), with an average detection probability of only 0.533. The average detection performance of the algorithm of this invention is 19.51% higher than that of the classic method.

[0081] This embodiment provides a method for time-frequency feature extraction and separation of frequency-hopping signals under multiple feature constraints, such as... Figure 1 As shown, the specific steps include: Step S1: Receive the external broadband mixed signal through the radio frequency receiving module, record the original parameters of the received signal, synchronously obtain the prior parameters of the target frequency hopping signal, select Chebyshev Type I bandpass filter as the core filter device, perform pre-filtering processing on the received broadband mixed signal, and output the filtered time domain signal. Step S2: Select STFT as the time-frequency image generation tool, calculate the optimal window length based on the prior parameters of the target frequency hopping signal with dual constraints, and output the time-frequency optimized grayscale time-frequency image; Step S3: Model the global and local grayscale features of the grayscale time-frequency image output in step S2. Based on the global and local grayscale features, design two dynamic thresholds, a high threshold and a low threshold, to construct a dual screening mechanism. Based on the binarization decision rule, repair the signal edge by judging the neighborhood correlation and output the binarized image. Step S4: Input the binarized image output in step S3, design the structural elements; after processing by opening and closing operations, introduce a morphological fault tolerance mechanism, quantify and verify the processing effect, and output a morphologically optimized binary image. Step S5: Detect the connected components in the morphologically optimized binary image output in step S4, construct a multi-feature constraint system, and use a progressive strategy to filter the target connected components; based on the time-frequency position of the target connected components, extract the original STFT time-frequency sub-matrix, restore it to the time domain signal segment through inverse STFT transformation, and splice it in time order to form a complete target frequency hopping signal.

[0082] Furthermore, in step S1, based on the fixed parameter characteristics of the target frequency-hopping signal, the frequency components corresponding to the target frequency-hopping signal are selectively retained, out-of-band noise and narrowband interference are filtered out, and the signal purity and signal-to-noise ratio in the subsequent time-frequency image generation stage are improved. This provides high-quality preprocessing input for the entire process of time-frequency feature extraction and separation of the frequency-hopping signal. Specifically, this is implemented as follows: Step S11: Receive external broadband mixed signals through the radio frequency receiving module. The broadband mixed signals include at least target frequency hopping signals, environmental thermal noise, fixed frequency interference, frequency sweeping interference, and burst pulse interference, covering typical interference types in complex electromagnetic environments. Record the raw parameters of the received signal, including the signal sampling frequency. and quantization bits, where the sampling frequency Strictly satisfying the Nyquist criterion, i.e. This ensures that the target signal is sampled without aliasing. The number of quantization bits is used to ensure the quantization accuracy of the signal and avoid signal feature distortion caused by quantization distortion.

[0083] The prior parameters of the target frequency-hopping signal are acquired synchronously. These prior parameters are inherent characteristic parameters of the target frequency-hopping signal and can be obtained through system presets or prior signal analysis and measurement. They include at least a fixed bandwidth B, a fixed pulse width T, and a preset center frequency. and frequency hopping interval This provides a parameter benchmark for subsequent signal processing; The target signal frequency range is defined, and coarse-grained energy detection is used to perform preliminary analysis of the broadband mixed signal. The coarse-grained energy detection is implemented by configuring a sliding window to traverse the signal frequency spectrum. The window length of the sliding window is adaptively set according to the minimum pulse width of the target frequency-hopping signal, and the window step size is 1 / 2 to 1 / 3 of the window length to ensure no signal energy peaks are missed. By statistically analyzing the frequency band energy values ​​corresponding to each window, the frequency corresponding to the energy peak is selected as the center frequency of the target frequency-hopping signal. This coarse-grained energy detection method is a simple way to quickly locate the main energy concentration band of a signal in engineering. It does not rely on precise signal parameters, but only needs to determine the energy peak value to quickly lock the center frequency. It balances detection efficiency and positioning accuracy, and provides a core basis for the accurate definition of the passband range of the subsequent bandpass filter.

[0084] Based on the fixed bandwidth B of the target frequency-hopping signal, the passband range of the bandpass filter is determined, denoted as:

[0085] in, It is the fixed bandwidth of the target frequency hopping signal. The center frequency of the target frequency hopping signal.

[0086] The passband range only allows the target frequency-hopping signal to pass through, suppressing interference signals and environmental noise outside the passband.

[0087] Step S12: Select a Chebyshev Type I bandpass filter as the core filter component to perform pre-filtering processing on the received broadband mixed signal; the Chebyshev Type I bandpass filter has the technical advantages of low passband ripple, fast stopband attenuation, and convenient engineering implementation, and can efficiently suppress out-of-band interference while ensuring that the amplitude and phase characteristics of the target signal are not distorted. The transfer function of the Chebyshev Type I bandpass filter is defined as:

[0088] in, The value is the passband ripple factor, which is set to satisfy passband ripple ≤ 1dB; The filter order is determined by the stopband attenuation requirement and the stopband cutoff frequency. It is an Nth-order Chebyshev polynomial; The center frequency of the target frequency hopping signal. The frequency value is the frequency component of the broadband mixed signal to be filtered.

[0089] Step S13: Configure the key parameters of the filter. The specific steps are as follows: The passband ripple coefficient ε is set to 0.1 to keep the amplitude fluctuation of the target signal within the passband within 1dB, ensuring that the amplitude characteristics of the target signal are not affected by the filtering process. According to the preset stopband attenuation requirements With stopband cutoff frequency Calculate the filter order using the formula The specific formula is as follows:

[0090] in, For stopband attenuation; B is the stopband cutoff frequency, and B is the fixed bandwidth. This represents the passband ripple factor. Define an Nth-order Chebyshev polynomial This provides mathematical support for the frequency response characteristics of the filter, ensuring stable and controllable filtering performance. The specific expression is:

[0091] Step S14: Based on the transfer function configured with the above parameters, two engineering-equivalent filtering implementation methods are provided to adapt to different application scenarios, and finally output a high signal-to-noise ratio time-domain filtered signal, including frequency domain implementation and time domain implementation. The frequency domain implementation method is used for the received broadband mixed signal. Perform a Fourier transform to obtain the frequency domain signal:

[0092] Where FT stands for Fourier transform; The frequency domain signal X( ) and the transfer function H( Perform a multiplication operation to obtain the filtered frequency domain signal:

[0093] To achieve signal retention within the passband and signal attenuation outside the passband; For the filtered frequency domain signal Performing the inverse Fourier transform yields the time-domain filtered signal:

[0094] Where IFT stands for Inverse Fourier Transform; The time-domain implementation method, for the transfer function Perform an inverse Fourier transform to obtain the impulse response of the filter;

[0095] Where IFT stands for Inverse Fourier Transform; Received broadband mixed signal With impulse response Performing convolution operations directly yields the time-domain filtered signal:

[0096] Where * represents convolution operation.

[0097] Save the filtered time-domain signal , as input signals for subsequent steps; The filtered time-domain signal The signal is stored as input for subsequent steps; the filtering effect is quantized and verified to ensure that the preprocessing step can improve the signal-to-noise ratio to a certain level. Horizontal; among which The total bandwidth of the received signal. The target signal bandwidth is defined; and the out-of-band redundant energy in the time-frequency image is effectively eliminated, meeting the signal quality requirements of subsequent time-frequency image processing.

[0098] Furthermore, step S2, through precise matching design of window length and fixed pulse width and fixed bandwidth of the target frequency hopping signal, generates a high-quality grayscale time-frequency spectrum image with balanced time-frequency resolution and complete target signal features, providing clear and distortion-free time-frequency image input for subsequent binarization, morphological processing, and feature selection; specifically including the following steps: Step S21: Select Short-Time Fourier Transform (STFT) as the time-frequency map generation tool. The STFT is used to represent the joint time-frequency distribution of the target signal. This transform has a simple principle, high computational efficiency, and is convenient for engineering implementation, making it suitable for real-time signal processing scenarios. The mathematical expression of STFT is defined as follows:

[0099] in, This is the filtered time-domain signal; Using the time window center as the sliding variable, the window function moves along the time axis to cover the entire signal duration; For window functions; This is a complex-valued time-frequency matrix, where each row corresponds to a time interval. Column corresponding to frequency , It is a complex exponential factor; Furthermore, a Hamming window is selected as the window function in this invention. The Hamming window has the characteristics of low spectral leakage and narrow main lobe, which can effectively preserve the time-frequency characteristics of the signal; its mathematical definition is:

[0100] in, The window length is the number of sampling points included in the window function. Taking the modulus of the complex-valued time-frequency matrix output by the STFT, we obtain | |, whose value corresponds to the time-frequency point The signal energy intensity at a given location is used to construct the grayscale time-frequency image required for subsequent processing.

[0101] Based on | | The grayscale time-frequency image after time-frequency optimization is constructed as follows:

[0102] in, For the number of pixels on the timeline, Number of pixels on the frequency axis; Step S22: Clarify the quantization requirements for time resolution and frequency resolution, ensuring that they match the fixed pulse width and fixed bandwidth of the target signal, respectively; specifically including: Based on window length and sampling frequency The time-frequency resolution of the STFT is defined to characterize the ability of the STFT to distinguish signals at different times, and directly determines the accuracy of capturing the pulse width of the target signal. Its mathematical expression is:

[0103] Based on window length and sampling frequency Frequency resolution is defined to characterize the ability of an STFT to distinguish signals of different frequencies, and directly determines the completeness of coverage of the target signal bandwidth. Its mathematical expression is:

[0104] Input the prior parameters of the target frequency-hopping signal, including a fixed pulse width T and a fixed bandwidth B; set the frequency axis oversampling coefficient k. 2. Ensure that the target signal bandwidth corresponds to at least two frequency pixels in the time-frequency graph to enhance feature distinguishability; fix the pulse width to match the target signal. With fixed bandwidth Window length It must meet two constraints, including frequency resolution constraint and pulse width matching constraint; The frequency resolution constraint is expressed as follows:

[0105] The pulse width matching constraint is expressed as follows:

[0106] in, Sampling frequency, Here, B is the frequency axis oversampling coefficient, B is the fixed bandwidth, and T is the fixed pulse width. For the length of the window, Frequency resolution; Will Substituting the rate of resolution constraint yields:

[0107] Combining pulse width matching constraints, the final window length is designed as follows:

[0108] in, This represents the floor function operator; This window length satisfies the balance requirements of time resolution and frequency resolution, ensuring both the integrity of pulse width capture and sufficient bandwidth coverage, while avoiding distortion of time and frequency characteristics.

[0109] Furthermore, the connected components of the target signal in the time-frequency diagram satisfy the following conditions: when At that time, the number of pixels on the time axis Precisely match pulse width; number of pixels on the frequency axis. , fully covering bandwidth B.

[0110] Furthermore, step S3 achieves dynamic threshold adjustment through joint modeling of global and local grayscale features. Combined with an 8-neighborhood correlation discrimination strategy, it accurately segments the signal and noise in the time-frequency image, repairs the signal edge breakage problem in low signal-to-noise ratio scenes, and provides a complete and clean binary image input for subsequent morphological processing. Specifically, it includes the following steps: Step S31: Perform time-frequency image grayscale feature modeling to provide quantization data support for dynamic threshold calculation. Specifically, this is implemented as follows: Define the grayscale time-frequency image Global grayscale mean μ and global variance The mathematical expressions are as follows:

[0111]

[0112] in, This represents the grayscale value of the pixel in the i-th row and j-th column, corresponding to the signal energy intensity at the time-frequency point (i,j). The larger the value, the more concentrated the signal energy at that time-frequency point. The global grayscale mean μ is used to quantify the average energy level of the entire time-frequency map, providing a basic reference benchmark for dual threshold calculation and preventing the threshold from deviating from the overall energy background. The global variance σ² is used to characterize the dispersion of all pixel grayscale values ​​relative to μ. The larger σ² is, the more significant the energy difference between signal and noise in the time-frequency map and the more uneven the grayscale distribution. Conversely, the smaller the σ² is, the smoother the grayscale distribution. This parameter provides a global basis for subsequent adjustment of the width of the threshold interval. The grayscale time-frequency image Divided into Non-overlapping local blocks ,satisfy:

[0113] Where P is the number of local blocks in the time axis direction and Q is the number of local blocks in the frequency axis direction. The values ​​of P and Q are determined through engineering experiments. The core principle is to ensure that the local blocks can capture local gray-scale differences without disrupting the connectivity of the target signal. The number of pixels on the time axis for a single local block. The frequency axis pixel count of a single local block is used to achieve non-overlapping division of the global image using the above equal division formula; The number of pixels on the time axis of the connected components of the target frequency hopping signal (determined by the fixed pulse width of the target signal and the STFT time resolution). The number of pixels on the frequency axis of the connected components of the target frequency hopping signal (determined by the fixed bandwidth of the target signal and the frequency resolution of the STFT). The constraint condition is essentially to ensure that each local block can fully accommodate the local region of the connected components of the target signal in both time and frequency dimensions, so as to avoid the target signal features being fragmented due to the small size of the local block, and to ensure that the local feature calculation can truly reflect the local grayscale characteristics of the target signal.

[0114] The local variance of the p-th and q-th local blocks is defined as:

[0115] in, For the p-th, q-th local block The local mean is used to quantify the average energy level of the local block, and complements the global mean μ. Let represent the set of pixel indices belonging to the p-th, q-th local block. This explicitly limits the calculation of the local variance to pixels within the current local block, avoiding interference from pixels across different regions. (Local variance) Used to characterize the dispersion of grayscale values ​​within a single local block, accurately capturing the differences in local energy distribution in different regions of the time-frequency map, for local blocks with concentrated signals. Larger; for noise-dominated local blocks, The parameter is relatively small, which provides key quantitative support for the local adaptive adjustment of the dual thresholds, enabling the thresholds to dynamically adapt to the grayscale distribution characteristics of different regions of the time-frequency map.

[0116] Step S32: Perform an adaptive dual threshold calculation operation based on local variance. Dynamic threshold adaptation is achieved through the fusion of global and local features. Specifically: Design a high threshold based on global and local grayscale features. With low threshold Two dynamic thresholds are used to construct a dual screening mechanism; The high threshold The mathematical expression is:

[0117] The low threshold The mathematical expression is:

[0118] in, , The coefficients were determined through grid search optimization. , This article adopts =2.0、 =0.8; , These are the maximum and minimum values ​​of the variance of all local blocks, respectively, used to reflect the non-uniformity of energy distribution in the time-frequency plot; The dynamism of the dual screening mechanism is reflected in the following: when the variance difference of local blocks is large (i.e., uneven energy distribution), the threshold range is adaptively widened; when the variance difference of local blocks is small, the threshold range is adaptively narrowed, ensuring threshold adaptability under different signal-to-noise ratio scenarios.

[0119] Step S33: Perform binarization decision rule operation, and repair signal edges through neighborhood correlation to ensure signal feature integrity. Specifically: Define a binarized image as:

[0120] in, =1 indicates a foreground signal pixel. =0 indicates background noise pixels.

[0121] The binary decision rule is:

[0122] in, express The 8-neighbor set of pixels (i.e., containing the 8 adjacent pixels around the point) If there are at least N pixels in the neighborhood that satisfy... Then the current pixel is determined to be a signal pixel. Otherwise, it is judged as a noise pixel. This rule addresses the issue of disconnected connected components under low signal-to-noise ratio conditions by utilizing neighborhood correlation, thus ensuring the integrity of signal characteristics.

[0123] Furthermore, in step S4, a rectangular structural element is designed using prior information about the fixed bandwidth and pulse width of the target signal. A morphological fault-tolerant mechanism is introduced, and through the collaborative processing of fault-tolerant opening operations and traditional closing operations, noise and bright spots are efficiently eliminated while ensuring the fidelity of signal edges and the integrity of key features, providing a clean and distortion-free binarized image input for subsequent connected component screening. Specifically, this includes the following steps: Step S41: Define and define the functions of basic morphological operations to provide a theoretical basis for processing. The specific implementation is as follows: Suppose the binarized image after step S3 The structural element is S, and the morphological corrosion is ( ) and expansion ( The operation is defined as follows:

[0124]

[0125] in, Image pixel coordinates, These are the coordinates of the structuring element.

[0126] Opening operation ( ) is defined as "corrosion followed by expansion", and the closing operation ( It is defined as "expansion followed by corrosion"; Step S42: Perform the design operation of the rectangular structural element, and achieve accurate matching between the structural element and the signal features based on the prior parameters of the target signal. Specifically: Based on the fixed bandwidth B and fixed pulse width T of the target frequency hopping signal, and the frequency axis resolution of the time-frequency image. Time axis resolution t; where the frequency axis resolution Defined as the frequency range corresponding to a unit pixel, time axis resolution t is defined as the time length corresponding to a unit pixel; set the rectangular structure element. ; Furthermore, set the width of the structural element. (Corresponding to the frequency axis), ensure that the width of the structural element is exactly the same as the number of pixels in the time-frequency image corresponding to the bandwidth of the target signal; the expression is:

[0127] Where B is the target signal bandwidth. Time-frequency image frequency axis resolution; Furthermore, set the height of the structural element. (Corresponding to the time axis), ensure that the height of the structuring element perfectly matches the number of pixels in the time-frequency image corresponding to the pulse width of the target signal. The expression is:

[0128] in, To fix the pulse width, t is the time axis resolution of the time-frequency image; The structuring element S adopts a solid rectangle design, meaning that all pixel values ​​within the structuring element are 1, and the coordinates of all pixels within the structuring element satisfy:

[0129] The core logic of this design lies in achieving the specificity of morphological operations through size matching: the erosion operation only eliminates elements smaller than a certain size. × The dilation operation only repairs edge defects in the connected domains of the target signal without damaging the target signal boundary; it does not cause fusion of connected domains of adjacent interfering signals. Furthermore, by adapting the size of the structuring element to the target signal, a morphological fault-tolerant mechanism is constructed, which can adapt to the localized small energy loss caused by channel attenuation in the measured signal, avoiding the problem of traditional general-purpose structuring elements misjudging the missing effective signal portion as noise.

[0130] Step S43: Perform collaborative optimization processing of fault-tolerant opening operation and traditional closing operation to achieve a balance between noise cancellation and signal fidelity. Specifically, this is implemented as follows: Define the binarized image after co-processing as , This method represents a morphologically optimized binary image; it removes noise and bright spots through tolerance-tolerant opening operations, while preserving the connectivity of local energy-deficient regions of the signal using tolerance-tolerant offset; then, it fills in internal holes and edge defects in the signal connected domains using traditional closing operations, thus repairing signal breakage problems in low signal-to-noise ratio scenarios; its transformation expression is:

[0131] Where S is a structural element; To quantify the processing effect, the signal edge fidelity F is defined as the degree of edge overlap between the processed image and the ideal binarized image (a noise-free and distortion-free binarized image of the target signal), expressed as:

[0132] in, For an ideal binarized image, The number of pixels on the time axis of the connected components of the target frequency hopping signal. The number of pixels on the frequency axis of the connected components of the target frequency hopping signal; When F ≥ 0.95, the signal edge distortion is determined to be less than 5%, which meets the signal morphology accuracy requirements for subsequent multi-feature joint screening; if F < 0.95, the structuring element size is fine-tuned. , (Adjustments not exceeding 1 pixel) Re-execute the collaborative operation until the fidelity requirement is met.

[0133] Furthermore, step S5, based on the prior information of the fixed parameters of the target frequency hopping signal, constructs a multi-feature constraint system, accurately identifies the target connected components through a progressive screening strategy, significantly reduces the false detection rate, and provides a clean and effective target region input for subsequent signal reconstruction. Specifically, it includes the following steps: Step S51: Perform connected component detection and core feature quantification definition operations to construct a multi-feature constraint system of "area + aspect ratio + average energy" to provide accurate quantitative basis for screening. Specifically, this is implemented as follows: exist The set of connected components detected in the middle is represented as Where K is the total number of connected components; for each connected component Define a multi-feature constraint system, including the area of ​​connected components, the aspect ratio of connected components, and the average energy of connected components; The area of ​​the connected component is defined as follows: The theoretical value for the total number of pixels contained is:

[0134] in, The number of pixels on the time axis of the connected components of the target frequency hopping signal. B is the number of pixels on the frequency axis of the connected components of the target frequency-hopping signal; B is the bandwidth of the target signal. Time-frequency image frequency axis resolution; To fix the pulse width, t is the time axis resolution of the time-frequency image; The tolerance range for the area of ​​connected components is set as follows in actual screening:

[0135] in, This is the lower tolerance limit. This is the upper tolerance limit; this paper adopts and .

[0136] The aspect ratio of the connected components is defined as follows: Frequency axis pixel count With time axis pixel count The ratio, its theoretical value is expressed as:

[0137] in, The number of pixels on the time axis of the connected components of the target frequency hopping signal. B is the number of pixels on the frequency axis of the connected components of the target frequency-hopping signal; B is the bandwidth of the target signal. Time-frequency image frequency axis resolution; To fix the pulse width, t is the time axis resolution of the time-frequency image; The aspect ratio tolerance range for connected components in actual filtering is set as follows:

[0138] in, ; This article adopts and .

[0139] The definition of the average energy of the connected components is as follows: The mean gray level of the corresponding region in the original time-frequency image is defined as:

[0140] in, The area of ​​the connected components; Set energy threshold ,in and These are the global mean and standard deviation of the time-frequency image, respectively, and the selection criteria are: .

[0141] Step S52: Execute a multi-feature progressive filtering strategy design to achieve accurate filtering of target connected components through hierarchical constraints, specifically as follows: A three-level screening logic of "initial screening - secondary screening - final screening" is constructed. Each level of screening is based on specific features to form constraints, gradually eliminating interfering connected components and retaining the target connected components. Initial screening based on the area of ​​connected components As a screening criterion, interfering connected components whose size differs significantly from the target signal are quickly eliminated, reducing the computational complexity of subsequent screening; the second screening is based on the aspect ratio of the connected components. As a screening criterion, interfering connected components that "match area but mismatch shape" are eliminated to strengthen the constraint on the rectangular shape of the target signal; the final screening is based on the average energy of the connected components. As the selection criterion, low-energy noise residue and weakly interfering connected components are filtered out to ensure that the retained connected components possess the high-energy concentration characteristics of the target signal; its mathematical expression is:

[0142] in, To set a tolerance range for the area of ​​connected components in actual screening. To set a tolerance range for the aspect ratio of connected components in actual screening. The average energy of the connected components. To set an energy threshold; Step S53: Based on the target connected component The time-frequency position is determined, and signal reconstruction is achieved through inverse time-frequency transformation. Let... The time interval corresponding to each connected component is (satisfy ), frequency range is (satisfy The refactoring process includes: From the original time-frequency matrix Extract the corresponding region submatrix ; Perform inverse STFT transformation:

[0143] in, For the time-domain reconstructed signal segment corresponding to the k-th target connected component, For window functions, This is a complex-valued time-frequency matrix, where each row corresponds to a time interval. Column corresponding to frequency t represents the reconstructed time point in the time domain.

[0144] The reconstructed signal segments corresponding to all connected components are spliced ​​together in time sequence to form a complete frequency hopping signal. .

[0145] The above-disclosed embodiments are merely preferred embodiments of the present invention, but the present invention is not limited thereto. Any non-creative variations that can be conceived by those skilled in the art, as well as any improvements and modifications made without departing from the principles of the present invention, should fall within the protection scope of the present invention.

Claims

1. A method for time-frequency feature extraction and separation of frequency-hopping signals under multi-feature constraints, characterized in that, Includes the following steps: Step S1: Receive the external broadband mixed signal through the radio frequency receiving module, record the original parameters of the received signal, synchronously obtain the prior parameters of the target frequency hopping signal, and select a bandpass filter to perform pre-filtering processing on the received broadband mixed signal. Output the filtered time-domain signal; Step S2: Select STFT as the time-frequency image generation tool, calculate the optimal window length based on the prior parameters of the target frequency hopping signal with dual constraints, and output the time-frequency optimized grayscale time-frequency image; Step S3: Model global and local grayscale features of the grayscale time-frequency image. Based on the global and local grayscale features, design two dynamic thresholds, a high threshold and a low threshold, to construct a dual screening mechanism. Based on the binarization decision rule, repair the signal edge by judging neighborhood correlation and output the binarized image. Step S4: Input a binary image and design structural elements; after processing through opening and closing operations, introduce a morphological fault tolerance mechanism to quantitatively verify the processing effect and output a morphologically optimized binary image. Step S5: Detect the connected components in the morphologically optimized binary image output in step S4, construct a multi-feature constraint system of "area + aspect ratio + average energy", and use a progressive strategy to screen the target connected components; based on the time-frequency position of the target connected components, extract the original STFT time-frequency sub-matrix, restore it to the time domain signal segment through inverse STFT transformation, and splice it in time order to form a complete target frequency hopping signal. In step S5, a multi-feature constraint system is constructed, specifically as follows: A three-level screening logic of "initial screening - secondary screening - final screening" is constructed. The initial screening is based on the tolerance range of the connected component area. As a screening criterion, the second screening is based on the aspect ratio tolerance range of the connected components. As the screening criterion, the final screening was based on the average energy of the connected components. The mathematical expression used for selection is: in, To set a tolerance range for the area of ​​connected components in actual screening. To set a tolerance range for the aspect ratio of connected components in actual screening. The average energy of the connected components. To set the energy threshold, For the target connected component, The tolerance limit is the area of ​​the connected components. This is the tolerance limit for the area of ​​the connected components. The theoretical value representing the aspect ratio of a connected component. This represents the area of ​​the connected components.

2. The method according to claim 1, characterized in that, In step S1, the bandpass filter is a Chebyshev type I bandpass filter, and its transfer function is: in, The value is the passband ripple factor, which is set to satisfy passband ripple ≤ 1dB; Let the filter order be . It is an Nth-order Chebyshev polynomial. The center frequency of the target frequency hopping signal. The frequency value of the frequency component in the broadband mixed signal to be filtered; In the transfer function of a Chebyshev type I bandpass filter, the Nth order Chebyshev polynomial The specific expression is: The filter order The specific formula is as follows: in, For stopband attenuation; B is the stopband cutoff frequency, and B is the fixed bandwidth. This represents the passband ripple coefficient.

3. The method according to claim 2, characterized in that, In step S1, a bandpass filter is selected to perform pre-filtering on the received broadband mixed signal; the filtered time-domain signal is output; the filtering can be implemented in both the frequency domain and the time domain. The frequency domain implementation method is used for the received broadband mixed signal. Perform a Fourier transform to obtain the frequency domain signal: Where FT stands for Fourier transform; The frequency domain signal X( ) and the transfer function H( Perform a multiplication operation to obtain the filtered frequency domain signal: For the filtered frequency domain signal Performing the inverse Fourier transform yields the time-domain filtered signal: Where IFT stands for Inverse Fourier Transform; The time-domain implementation method, for the transfer function Perform an inverse Fourier transform to obtain the impulse response of the filter; Where IFT stands for Inverse Fourier Transform; Received broadband mixed signal With impulse response Perform convolution operation to obtain the time-domain filtered signal: in, This represents the convolution operation; Save the filtered time-domain signal This serves as the input signal for subsequent steps.

4. The method according to claim 3, characterized in that, In step S2, the mathematical expression for STFT is: in, This is the filtered time-domain signal; Using the time window center as the sliding variable, the window function moves along the time axis to cover the entire signal duration; For window functions; This is a complex-valued time-frequency matrix, where each row corresponds to a time interval. Column corresponding to frequency , It is a complex exponential factor; Hamming window is selected as the window function. The mathematical definition is: in, The window length is the number of sampling points included in the window function.

5. The method according to claim 4, characterized in that, In step S2, the calculation of the optimal window length based on the dual constraints of setting prior parameters of the target frequency hopping signal specifically includes: The STFT time-frequency resolution is defined mathematically as follows: in, For the length of the window, The sampling frequency; Frequency resolution is defined mathematically as follows: in, For the length of the window, The sampling frequency; The window length is designed as follows: in, This represents the floor function. For the length of the window, Sampling frequency, is the frequency axis oversampling coefficient, and B is the fixed bandwidth.

6. The method according to claim 5, characterized in that, In step S3, the high threshold The mathematical expression is: The low threshold The mathematical expression is: in, , The coefficients were determined through grid search optimization, where μ is the global grayscale mean. , ; , These are the maximum and minimum values ​​of the global variance and the variance of all local blocks, respectively.

7. The method according to claim 6, characterized in that, In step S3, the binarization decision rule is: in, This represents the grayscale value of the pixel in the i-th row and j-th column. express The set of 8 neighboring pixels; if there are at least N pixels in the neighborhood that satisfy Then the current pixel is determined to be a signal pixel. Otherwise, it is judged as a noise pixel. .

8. The method according to claim 7, characterized in that, In step S4, the opening and closing operation expression is: Where S is the structural element. For binarized images, Represents a morphologically optimized binary image; The opening operation is defined as erosion followed by dilation. For the closing operation, it is defined as first expanding and then eroding; The morphological erosion and dilation operations are defined as follows: in, Image pixel coordinates, For the coordinates of the structuring element, For erosion calculation, For expansion, This is the binarized image after collaborative processing.

9. The method according to claim 8, characterized in that, In step S5, the specific expression for the inverse STFT transformation is: in, This is a submatrix of the corresponding region in the original time-frequency matrix. For the time-domain reconstructed signal segment corresponding to the k-th target connected component, For window functions, This is a complex-valued time-frequency matrix, where each row corresponds to a time interval. Column corresponding to frequency ; t represents the reconstructed time point in the time domain. It is a complex exponential factor.

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